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S/MIME Working Group                                          B. Kaliski
Internet Draft                                          RSA Laboratories
Document: draft-ietf-smime-cms-rsa-kem-01.txt               October 2003
Category: Standards


           Use of the RSA-KEM Key Transport Algorithm in CMS
                 <draft-ietf-smime-cms-rsa-kem-01.txt>


Status of this Memo

   This document is an Internet-Draft and is subject to all provisions
   of Section 10 of RFC2026.

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Abstract

   The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward)
   mechanism for transporting keying data to a recipient using the
   recipient's RSA public key. This document specifies the conventions
   for using the RSA-KEM Key Transport Algorithm with the Cryptographic
   Message Syntax (CMS). This version (-01) updates the ASN.1 syntax to
   align with the latest drafts of ANS X9.44 and ISO/IEC 18033-2, and
   adds material on certificate conventions and S/MIME capabilities.

Conventions Used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED",  "MAY", and "OPTIONAL" in
   this document are to be interpreted as described in RFC 2119
   [STDWORDS].




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1. Introduction

   The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward)
   mechanism for transporting keying data to a recipient using the
   recipient's RSA public key.

   Most previous key transport algorithms based on the RSA public-key
   cryptosystem (e.g., the popular PKCS #1 v1.5 algorithm [PKCS1]) have
   the following general form:

      1. Format or "pad" the keying data to obtain an integer m.

      2. Encrypt the integer m with the recipient's RSA public key:

                                c = m^e mod n

      3. Output c as the encrypted keying data.

   The RSA-KEM Key Transport Algorithm takes a different approach that
   provides higher security assurance, by encrypting a _random_ integer
   with the recipient's public key, and using a symmetric key-wrapping
   scheme to encrypt the keying data. It has the following form:

      1. Generate a random integer z between 0 and n-1.

      2. Encrypt the integer z with the recipient's RSA public key:

                                c = z^e mod n.

      3. Derive a key-encrypting key KEK from the integer z.

      4. Wrap the keying data using KEK to obtain wrapped keying data
         WK.

      5. Output c and WK as the encrypted keying data.

   This different approach provides higher security assurance because
   the input to the underlying RSA operation is random and independent
   of the message, and the key-encrypting key KEK is derived from it in
   a strong way. As a result, the algorithm enjoys a "tight" security
   proof in the random oracle model. It is also architecturally
   convenient because the public-key operations are separate from the
   symmetric operations on the keying data. One benefit is that the
   length of the keying data is bounded only by the symmetric key-
   wrapping scheme, not the size of the RSA modulus.

   The RSA-KEM Key Transport Algorithm in various forms is being adopted
   in several draft standards including the draft ANS X9.44 [ANS-X9.44]
   and the draft ISO/IEC 18033-2 [ISO-IEC-18033-2]. It has also been
   recommended by the NESSIE project [NESSIE]. Although the other
   standards are still in development, the algorithm is stable across
   the drafts. For completeness, a specification of the algorithm is
   given in Appendix A of this document; ASN.1 syntax is given in

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   Appendix B.

   NOTE: The term KEM stands for "key encapsulation mechanism" and
   refers to the first three steps of the process above. The
   formalization of key transport algorithms (or more generally,
   asymmetric encryption schemes) in terms of key encapsulation
   mechanisms is described further in research by Victor Shoup leading
   to the development of the ISO/IEC 18033-2 standard [SHOUP].

2. Use in CMS

   The RSA-KEM Key Transport Algorithm MAY be employed for one or more
   recipients in the CMS enveloped-data content type (Section 6 of
   [CMS]), where the keying data processed by the algorithm is the CMS
   content-encryption key.

   The RSA-KEM Key Transport Algorithm SHOULD be considered for new
   CMS-based applications as a replacement for the widely implemented
   RSA encryption algorithm specified originally in PKCS #1 v1.5 (see
   [PKCS1] and Section 4.2.1 of [CMSALGS]), which is vulnerable to
   chosen-ciphertext attacks. The RSAES-OAEP Key Transport Algorithm
   has also been proposed as a replacement (see [PKCS1] and [CMS-
   OAEP]). RSA-KEM has the advantage over RSAES-OAEP of a tighter
   security proof, but the disadvantage of slightly longer encrypted
   keying data.

2.1 Underlying Components

   A CMS implementation that supports the RSA-KEM Key Transport
   Algorithm MUST support at least the following underlying components:

      *  For the key derivation function, KDF2 (see [ANS-X9.44][IEEE-
         P1363a]) based on SHA-1 (see [FIPS-180-2]) (this function is
         also specified as the key derivation function in [ANS-X9.63])

      *  For the key-wrapping scheme, AES-Wrap-128, i.e., the AES Key
         Wrap with a 128-bit key encrypting key (see [AES-WRAP])

   An implementation SHOULD also support KDF2 based on SHA-256 (see
   [FIPS-180-2]), and the Triple-DES Key Wrap (see [3DES-WRAP]). It MAY
   support other underlying components.

2.2 RecipientInfo Conventions

   When the RSA-KEM Key Transport Algorithm is employed for a recipient,
   recipient, the RecipientInfo alternative for that recipient MUST be
   KeyTransRecipientInfo. The algorithm-specific fields of the
   KeyTransRecipientInfo value MUST have the following values:

      *  keyEncryptionAlgorithm.algorithm MUST be id-ac-generic-hybrid
         (see Appendix B)



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      *  keyEncryptionAlgorithm.parameters MUST be a value of type
         GenericHybridParameters, identifying the RSA-KEM key
         encapsulation mechanism (see Appendix B)

      *  encryptedKey MUST be the encrypted keying data output by the
         algorithm (see Appendix A)

2.3 Certificate Conventions

   The conventions specified in this section augment RFC 3280 [PROFILE].

   A recipient who employs the RSA-KEM Key Transport Algorithm MAY
   identify the public key in a certificate by the same
   AlgorithmIdentifier as for the PKCS #1 v1.5 algorithm, i.e., using
   the rsaEncryption object identifier [PKCS1].

   If the recipient wishes only to employ the RSA-KEM Key Transport
   Algorithm with a given public key, the recipient MUST identify the
   public key in the certificate using the id-ac-generic-hybrid object
   identifier (see Appendix B) where the associated
   GenericHybridParameters value indicates the underlying components
   with which the algorithm is to be employed. The certificate user MUST
   perform the RSA-KEM Key Transport algorithm using only those
   components.

   Regardless of the AlgorithmIdentifier used, the RSA public key is
   encoded in the same manner in the subject public key information.
   The RSA public key MUST be encoded using the type RSAPublicKey type:

      RSAPublicKey ::= SEQUENCE {
         modulus            INTEGER, -- n
         publicExponent     INTEGER  -- e
      }

   Here, the modulus is the modulus n, and publicExponent is the public
   exponent e. The DER encoded RSAPublicKey is carried in the
   subjectPublicKey BIT STRING within the subject public key
   information.

   The intended application for the key MAY be indicated in the key
   usage certificate extension (see [PROFILE], Section 4.2.1.3). If the
   keyUsage extension is present in a certificate that conveys an RSA
   public key with the id-ac-generic-hybrid object identifier as
   discussed above, then the key usage extension MUST contain the
   following value:

      keyEncipherment.

   dataEncipherment SHOULD NOT be present. That is, a key intended to be
   employed only with the RSA-KEM Key Transport Algorithm SHOULD NOT
   also be employed for data encryption.



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2.4 SMIMECapabilities Attribute Conventions

   RFC 2633 [MSG], Section 2.5.2 defines the SMIMECapabilities signed
   attribute (defined as a SEQUENCE of SMIMECapability SEQUENCEs) to be
   used to specify a partial list of algorithms that the software
   announcing the SMIMECapabilities can support. When constructing a
   signedData object, compliant software MAY include the
   SMIMECapabilities signed attribute announcing that it supports the
   RSA-KEM Key Transport algorithm.

   The SMIMECapability SEQUENCE representing the RSA-KEM Key Transport
   Algorithm MUST include the id-ac-generic-hybrid object identifier
   (see Appendix B) in the capabilityID field and MUST include a
   GenericHybridParameters value in the parameters field identifying the
   components with which the algorithm is to be employed.

   The DER encoding of a SMIMECapability SEQUENCE is the same as the DER
   encoding of an AlgorithmIdentifier. Example DER encodings for typical
   sets of components are given in Appendix B.4.


3. Security Considerations

   The security of the RSA-KEM Key Transport Algorithm described in
   this document can be shown to be tightly related to the difficulty
   of either solving the RSA problem or breaking the underlying
   symmetric key-wrapping scheme, if the underlying key derivation
   function is modeled as a random oracle, and assuming that the
   symmetric key-wrapping scheme satisfies the properties of a data
   encapsulation mechanism [SHOUP]. While in practice a random-oracle
   result does not provide an actual security proof for any particular
   key derivation function, the result does provide assurance that the
   general construction is reasonable; a key derivation function would
   need to be particularly weak to lead to an attack that is not
   possible in the random oracle model.

   The RSA key size and the underlying components should be selected
   consistent with the desired symmetric security level for an
   application. Several security levels have been identified in [NIST-
   GUIDELINE]. For brevity, the first three levels are mentioned here:

      *  80-bit security. The RSA key size SHOULD be at least 1024 bits,
         the hash function underlying KDF2 SHOULD be SHA-1 or above, and
         the symmetric key-wrapping scheme SHOULD be AES Key Wrap or
         Triple-DES Key Wrap.

      *  112-bit security. The RSA key size SHOULD be at least 2048
         bits, the hash function underlying KDF2 SHOULD be SHA-224 or
         above, and the symmetric key-wrapping scheme SHOULD be AES Key
         Wrap or Triple-DES Key Wrap.

      *  128-bit security. The RSA key size SHOULD be at least 3072
         bits, the hash function underlying KDF2 SHOULD be SHA-256 or

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         above, and the symmetric key-wrapping scheme SHOULD be AES Key
         Wrap.

   Note that the AES Key Wrap MAY be used at all three of these levels;
   the use of AES does not require a 128-bit security level for other
   components.

   Implementations MUST protect the RSA private key and the content-
   encryption key. Compromise of the RSA private key may result in the
   disclosure of all messages protected with that key. Compromise of the
   content-encryption key may result in disclosure of the associated
   encrypted content.

   Additional considerations related to key management may be found in
   [NIST-GUIDELINE].

   The security of the algorithm also depends on the strength of the
   random number generator, which SHOULD have a comparable security
   level. For further discussion on random number generation, please
   see [RANDOM].

   Implementations SHOULD NOT reveal information about intermediate
   values or calculations, whether by timing or other "side channels",
   or otherwise an opponent may be able to determine information about
   the keying data and/or the recipient's private key. Although not all
   intermediate information may be useful to an opponent, it is
   preferable to conceal as much information as is practical, unless
   analysis specifically indicates that the information would not be
   useful.

   Generally, good cryptographic practice employs a given RSA key pair
   in only one scheme.  This practice avoids the risk that vulnerability
   in one scheme may compromise the security of the other, and may be
   essential to maintain provable security.  While RSA public keys have
   often been employed for multiple purposes such as key transport and
   digital signature without any known bad interactions, for increased
   security assurance, such combined use of an RSA key pair is NOT
   RECOMMENDED in the future (unless the different schemes are
   specifically designed to be used together).

   Accordingly, an RSA key pair used for the RSA-KEM Key Transport
   Algorithm SHOULD NOT also be used for digital signatures. (Indeed,
   ASC X9 requires such a separation between key establishment key pairs
   and digital signature key pairs.) Continuing this principle of key
   separation, a key pair used for the RSA-KEM Key Transport Algorithm
   SHOULD NOT be used with other key establishment schemes, or for data
   encryption, or with more than one set of underlying algorithm
   components.

   Parties MAY wish to formalize the assurance that one another's
   implementations are correct through implementation validation, e.g.
   NIST's Cryptographic Module Validation Program (CMVP).


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4. References

4.1 Normative References

   3DES-WRAP         Housley, R. Triple-DES and RC2 Key Wrapping. RFC
                     3217. December 2001.

   AES-WRAP          Schaad, J. and R. Housley. Advanced Encryption
                     Standard (AES) Key Wrap Algorithm. RFC 3394.
                     September 2002.

   ANS-X9.63         American National Standard X9.63-2002: Public Key
                     Cryptography for the Financial Services Industry:
                     Key Agreement and Key Transport Using Elliptic
                     Curve Cryptography.

   CMS               Housley, R. Cryptographic Message Syntax. RFC
                     3369. August 2002.

   CMSALGS           Housley, R. Cryptographic Message Syntax (CMS)
                     Algorithms. RFC 3370. August 2002.

   FIPS-180-2        National Institute of Standards and Technology
                     (NIST). FIPS 180-2: Secure Hash Standard. August
                     2002.

   MSG               Ramsdell, B. S/MIME Version 3 Message
                     Specification. RFC 2633. June 1999.

   PROFILE           Housley, R., Polk, W., Ford, W. and D. Solo.
                     Internet X.509 Public Key Infrastructure:
                     Certificate and Certificate Revocation List (CRL)
                     Profile. RFC 3280. April 2002.

   STDWORDS          Bradner, S. Key Words for Use in RFCs to Indicate
                     Requirement Levels. RFC 2119. March 1997.

4.2 Informative References

   ANS-X9.44         ASC X9F1 Working Group. Draft American National
                     Standard X9.44: Public Key Cryptography for the
                     Financial Services Industry -- Key Establishment
                     Using Integer Factorization Cryptography. Draft D6,
                     October 15, 2003.

   CMS-OAEP          Housley, R. Use of the RSAES-OAEP Key Transport
                     Algorithm in the Cryptographic Message Syntax
                     (CMS). RFC 3560. July 2003.

   IEEE-P1363a       IEEE P1363 Working Group. IEEE P1363a: Standard
                     Specifications for Public Key Cryptography:
                     Additional Techniques. Draft D12, May 12, 2003.
                     Available via http://grouper.ieee.org/groups/1363.

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   ISO-IEC-18033-2   ISO/IEC 18033-2: Information technology -- Security
                     techniques -- Encryption algorithms – Part 2:
                     Asymmetric Ciphers. 2nd Committee Draft, July 10,
                     2003.

   NESSIE            NESSIE Consortium. Portfolio of Recommended
                     Cryptographic Primitives. February 27, 2003.
                     Available via http://www.cryptonessie.org/.

   NIST-GUIDELINE    National Institute of Standards and Technology.
                     Special Publication 800-57: Recommendation for Key
                     Management. Part 1: General Guideline. Draft,
                     January 2003. Available via
                     http://csrc.nist.gov/CryptoToolkit/tkkeymgmt.html.

   PKCS1             Jonsson, J. and B. Kaliski. PKCS #1: RSA
                     Cryptography Specifications Version 2.1. RFC 3447.
                     February 2003.

   RANDOM            Eastlake, D., S. Crocker, and J. Schiller.
                     Randomness Recommendations for Security. RFC 1750.
                     December 1994.

   SHOUP             Shoup, V. A Proposal for an ISO Standard for
                     Public Key Encryption. Version 2.1, December 20,
                     2001. Available via http://www.shoup.net/papers/.


5. IANA Considerations

   Within the CMS, algorithms are identified by object identifiers
   (OIDs). With one exception, all of the OIDs used in this document
   were assigned in other IETF documents, in ISO/IEC standards
   documents, by the National Institute of Standards and Technology
   (NIST), and in Public-Key Cryptography Standards (PKCS) documents.
   The one exception is that the ASN.1 module's identifier (see Appendix
   B.3) is assigned in this document. No further action by the IANA is
   necessary for this document or any anticipated updates.


6. Acknowledgments

   This document is one part of a strategy to align algorithm standards
   produced by ASC X9, ISO/IEC JTC1 SC27, NIST, and the IETF. I would
   like to thank the members of the ASC X9F1 working group for their
   contributions to drafts of ANS X9.44 which led to this specification.
   My thanks as well to Russ Housley as well for his guidance and
   encouragement. I also appreciate the helpful direction I've received
   from Blake Ramsdell and Jim Schaad in bringing this document to
   fruition.




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7. Author's Address

   Burt Kaliski
   RSA Laboratories
   174 Middlesex Turnpike
   Bedford, MA  01730
   USA
   bkaliski@rsasecurity.com


Appendix A. RSA-KEM Key Transport Algorithm

   The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward)
   mechanism for transporting keying data to a recipient using the
   recipient's RSA public key.

   With this type of algorithm, a sender encrypts the keying data using
   the recipient's public key to obtain encrypted keying data. The
   recipient decrypts the encrypted keying data using the recipient's
   private key to recover the keying data.

A.1 Underlying Components

   The algorithm has the following underlying components:

       * KDF, a key derivation function, which derives keying data of a
         specified length from a shared secret value

       * Wrap, a symmetric key-wrapping scheme, which encrypts keying
         data using a key-encrypting key

   In the following, kekLen denotes the length in bytes of the key-
   encrypting key for the underlying symmetric key-wrapping scheme.

   In this scheme, the length of the keying data to be transported MUST
   be among the lengths supported by the underlying symmetric key-
   wrapping scheme. (The AES Key Wrap, for instance, requires the length
   of the keying data to be a multiple of 8 bytes, and at least 16
   bytes.) Usage and formatting of the keying data (e.g., parity
   adjustment for Triple-DES keys) is outside the scope of this
   algorithm.

   With some key derivation functions, it is possible to include other
   information besides the shared secret value in the input to the
   function. Also, with some symmetric key-wrapping schemes, it is
   possible to associate a label with the keying data. Such uses are
   outside the scope of this document, as they are not directly
   supported by CMS.

A.2 Sender's Operations

   Let (n,e) be the recipient's RSA public key (see [PKCS1] for details)
   and let K be the keying data to be transported.

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   Let nLen denote the length in bytes of the modulus n, i.e., the least
   integer such that 2^{8*nLen} > n.

   The sender performs the following operations:

      1. Generate a random integer z between 0 and n-1 (see Note), and
         convert z to a byte string Z of length nLen, most significant
         byte first:

                          z = RandomInteger (0, n-1)
                         Z = IntegerToString (z, nLen)

      2. Encrypt the random integer z using the recipient's public key
         (n,e) and convert the resulting integer c to a ciphertext C, a
         byte string of length nLen:

                                 c = z^e mod n
                         C = IntegerToString (c, nLen)

      3. Derive a key-encrypting key KEK of length kekLen bytes from the
         byte string Z using the underlying key derivation function:

                             KEK = KDF (Z, kekLen)

      4. Wrap the keying data K with the key-encrypting key KEK using
         the underlying key-wrapping scheme to obtain wrapped keying
         data WK:

                              WK = Wrap (KEK, K)

     5. Concatenate the ciphertext C and the wrapped keying data WK to
        obtain the encrypted keying data EK:

                                 EK = C || WK

      6. Output the encrypted keying data EK.

   NOTE: The random integer z MUST be generated independently at random
   for different encryption operations, whether for the same or
   different recipients.

A.3 Recipient's Operations

   Let (n,d) be the recipient's RSA private key (see [PKCS1]; other
   private key formats are allowed) and let EK be the encrypted keying
   data.

   Let nLen denote the length in bytes of the modulus n.

   The recipient performs the following operations:

      1. Separate the encrypted keying data EK into a ciphertext C of
         length nLen bytes and wrapped keying data WK:

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                                 C || WK = EK

         If the length of the encrypted keying data is less than nLen
         bytes, output "decryption error" and stop.

      2. Convert the ciphertext C to an integer c, most significant
         byte first. Decrypt the integer c using the recipient's
         private key (n,d) to recover an integer z (see Note):

                            c = StringToInteger (C)
                                 z = c^d mod n

         If the integer c is not between 0 and n-1, output "decryption
         error" and stop.

      3. Convert the integer z to a byte string Z of length nLen, most
         significant byte first (see Note):

                         Z = IntegerToString (z, nLen)

      4. Derive a key-encrypting key KEK of length kekLen bytes from
         the byte string Z using the underlying key derivation function
         (see Note):

                             KEK = KDF (Z, kekLen)

      5. Unwrap the wrapped keying data WK with the key-encrypting key
         KEK using the underlying key-wrapping scheme to recover the
         keying data K:

                             K = Unwrap (KEK, WK)

         If the unwrapping operation outputs an error, output
         "decryption error" and stop.

      6. Output the keying data K.

   NOTE: Implementations SHOULD NOT reveal information about the integer
   z and the string Z, nor about the calculation of the exponentiation
   in Step 2, the conversion in Step 3, or the key derivation in Step 4,
   whether by timing or other "side channels". The observable behavior
   of the implementation SHOULD be the same at these steps for all
   ciphertexts C that are in range. (For example, IntegerToString
   conversion should take the same amount of time regardless of the
   actual value of the integer z.) The integer z, the string Z and other
   intermediate results MUST be securely deleted when they are no longer
   needed.


Appendix B. ASN.1 Syntax

   The ASN.1 syntax for identifying the RSA-KEM Key Transport Algorithm
   is an extension of the syntax for the "generic hybrid cipher" in the

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   draft ISO/IEC 18033-2 [ISO-IEC-18033-2], and is the same as employed
   in the draft ANS X9.44 [ANS-X9.44]. The syntax for the scheme is
   given in Section B.1. The syntax for selected underlying components
   including those mentioned above is given in B.2.

   The following object identifier prefixes are used in the definitions
   below:

      is18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) }

      nistAlgorithm OID ::= {
         joint-iso-itu-t(2) country(16) us(840) organization(1)
         gov(101) csor(3) nistAlgorithm(4)
      }

      pkcs-1 OID ::= {
         iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1)
      }

   NullParms is a more descriptive synonym for NULL when an algorithm
   identifier has null parameters:

      NullParms ::= NULL

   The material in this Appendix is based on a draft standard and is
   SUBJECT TO CHANGE as that standard is developed.

B.1 RSA-KEM Key Transport Algorithm

   The object identifier for the RSA-KEM Key Transport Algorithm is the
   same as for the "generic hybrid cipher" in the draft ANS ISO/IEC
   18033-2, id-ac-generic-hybrid, which is defined in the draft as

      id-ac-generic-hybrid OID ::= {
         is18033-2 asymmetric-cipher(1) generic-hybrid(2)
      }

   The associated parameters for id-ac-generic-hybrid have type
   GenericHybridParameters:

      GenericHybridParameters ::= {
         kem  KeyEncapsulationMechanism,
         dem  DataEncapsulationMechanism
      }

   The fields of type GenericHybridParameters have the following
   meanings:

      *  kem identifies the underlying key encapsulation mechanism. For
         the RSA-KEM Key Transport Algorithm, the scheme is RSA-KEM from
         the draft ISO/IEC 18033-2.

         The object identifier for RSA-KEM (as a key encapsulation

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         mechanism) is id-kem-rsa, which is defined in the draft ISO/IEC
         18033-2 as

            id-kem-rsa OID ::= {
               is18033-2 key-encapsulation-mechanism(2) rsa(4)
            }

         The associated parameters for id-kem-rsa have type
         RsaKemParameters:

            RsaKemParameters ::= {
              keyDerivationFunction  KeyDerivationFunction,
              keyLength              KeyLength
            }

         The fields of type RsaKemParameters have the following
         meanings:

            *  keyDerivationFunction identifies the underlying key
               derivation function. For alignment with the draft ANS
               X9.44, it MUST be KDF2. However, other key derivation
               functions MAY be used with CMS. Please see B.2.1 for the
               syntax for KDF2.

                  KeyDerivationFunction ::=
                     AlgorithmIdentifier {{KDFAlgorithms}}

                  KDFAlgorithms ALGORITHMS ::= {
                     kdf2,
                     ...  -- implementations may define other methods
                  }

            *  keyLength is the length in bytes of the key-encrypting
               key, which depends on the underlying symmetric key-
               wrapping scheme.

                  KeyLength ::= INTEGER (1..MAX)

      *  dem identifies the underlying data encapsulation mechanism.
         For alignment with the draft ANS X9.44, it MUST be an X9-
         approved symmetric key-wrapping scheme. (See Note.) However,
         other symmetric key-wrapping schemes MAY be used with CMS.
         Please see B.2.2 for the syntax for the AES and Triple-DES Key
         Wraps.

            DataEncapsulationMechanism ::=
               AlgorithmIdentifier {{DEMAlgorithms}}

            DEMAlgorithms ALGORITHM ::= {
               X9-SymmetricKeyWrappingSchemes,
               ...  -- implementations may define other methods
            }


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            X9-SymmetricKeyWrappingSchemes ALGORITHM ::= {
               aes128-Wrap | aes192-Wrap | aes256-Wrap | tdes-Wrap,
               ...   -- allows for future expansion
            }

   NOTE: The generic hybrid cipher in the draft ISO/IEC 18033-2 can
   encrypt arbitrary data, hence the term "data encapsulation
   mechanism". The symmetric key-wrapping schemes take the role of data
   encapsulation mechanisms in the RSA-KEM Key Transport Algorithm. The
   draft ISO/IEC 18033-2 currently allows only three particular data
   encapsulation mechanisms, not including any of these symmetric key-
   wrapping schemes. However, the ASN.1 syntax in that document expects
   that additional algorithms will be allowed.

B.2 Selected Underlying Components

B.2.1 Key Derivation Functions

   The object identifier for KDF2 (see [ISO-IEC-18033-2]) is

      id-kdf-kdf2 OID ::= {
         is18033-2 key-derivation-functions(5) kdf2(2)
      }

   The associated parameters identify the underlying hash function. For
   alignment with the draft ANS X9.44, the hash function MUST be an ASC
   X9-approved hash function. (See Note.) However, other hash functions
   MAY be used with CMS.

      kdf2 ALGORITHM ::= {{ OID id-kdf-kdf2  PARMS KDF2-HashFunction }}

      KDF2-HashFunction ::= AlgorithmIdentifier {{KDF2-HashFunctions}}

      KDF2-HashFunctions ALGORITHM ::= {
         X9-HashFunctions,
         ...  -- implementations may define other methods
      }

      X9-HashFunctions ALGORITHM ::= {
         sha1 | sha224 | sha256 | sha384 | sha512,
         ...  -- allows for future expansion
      }

   The object identifier for SHA-1 is

      id-sha1 OID ::= {
         iso(1) identified-organization(3) oiw(14) secsig(3)
         algorithms(2) sha1(26)
     }

   The object identifiers for SHA-256, SHA-384 and SHA-512 are

      id-sha256 OID ::= { nistAlgorithm hashAlgs(2) sha256(1) }

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      id-sha384 OID ::= { nistAlgorithm hashAlgs(2) sha384(2) }
      id-sha512 OID ::= { nistAlgorithm hashAlgs(2) sha512(3) }

   There has been some confusion over whether the various SHA object
   identifiers have a NULL parameter, or no associated parameters. As
   also discussed in [PKCS1], implementations SHOULD generate algorithm
   identifiers without parameters, and MUST accept algorithm identifiers
   either without parameters, or with NULL parameters.

      sha1   ALGORITHM ::= {{ OID id-sha1   }} -- NULLParms MUST be
      sha224 ALGORITHM ::= {{ OID id-sha224 }} -- accepted for these
      sha256 ALGORITHM ::= {{ OID id-sha256 }} -- OIDs
      sha384 ALGORITHM ::= {{ OID id-sha384 }} –- ""
      sha512 ALGORITHM ::= {{ OID id-sha512 }} –- ""

   NOTE: As of this writing, only SHA-1 is an ASC X9-approved hash
   function; SHA-224 and above are in the process of being approved. The
   object identifier for SHA-224 has not yet been assigned.

B.2.2 Symmetric Key-Wrapping Schemes

   The object identifiers for the AES Key Wrap depends on the size of
   the key encrypting key. There are three object identifiers (see
   [AES-WRAP]):

      id-aes128-Wrap OID ::= { nistAlgorithm aes(1) aes128-Wrap(5)  }
      id-aes192-Wrap OID ::= { nistAlgorithm aes(1) aes192-Wrap(25) }
      id-aes256-Wrap OID ::= { nistAlgorithm aes(1) aes256-Wrap(45) }

   These object identifiers have no associated parameters.

      aes128-Wrap ALGORITHM ::= {{ OID id-aes128-wrap }}
      aes192-Wrap ALGORITHM ::= {{ OID id-aes192-wrap }}
      aes256-Wrap ALGORITHM ::= {{ OID id-aes256-wrap }}

   The object identifier for the Triple-DES Key Wrap (see [3DES-WRAP])
   is

      id-alg-CMS3DESwrap OBJECT IDENTIFIER ::= {
         iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9)
         smime(16) alg(3) 6
      }

   This object identifier has a NULL parameter.

      tdes-Wrap ALGORITHM ::=
         {{ OID id-alg-CMS3DESwrap  PARMS NullParms }}

   NOTE: As of this writing, the AES Key Wrap and the Triple-DES Key
   Wrap are in the process of being approved by ASC X9.




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B.3 ASN.1 module

   CMS-RSA-KEM
      { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
        pkcs-9(9) smime(16) modules(0) cms-rsa-kem(21) } [[check]]

   BEGIN

   -- EXPORTS ALL

   -- IMPORTS None

   -- Useful types and definitions

   OID ::= OBJECT IDENTIFIER  -- alias

   -- Unless otherwise stated, if an object identifier has associated
   -- parameters (i.e., the PARMS element is specified), the parameters
   -- field shall be included in algorithm identifier values. The
   -- parameters field shall be omitted if and only if the object
   -- identifier does not have associated parameters (i.e., the PARMS
   -- element is omitted), unless otherwise stated.

   ALGORITHM ::= CLASS {
      &id    OBJECT IDENTIFIER  UNIQUE,
      &Type  OPTIONAL
   }
   WITH SYNTAX { OID &id [PARMS &Type] }

   AlgorithmIdentifier { ALGORITHM:IOSet } ::= SEQUENCE {
      algorithm   ALGORITHM.&id( {IOSet} ),
      parameters  ALGORITHM.&Type( {IOSet}{@algorithm} )  OPTIONAL
   }

   NullParms ::= NULL

   -- ISO/IEC 18033-2 arc

   is18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) }

   -- NIST algorithm arc

   nistAlgorithm OID ::= {
      joint-iso-itu-t(2) country(16) us(840) organization(1)
      gov(101) csor(3) nistAlgorithm(4)
   }

   -- PKCS #1 arc

   pkcs-1 OID ::= {
      iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1)
   }


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   -- RSA-KEM Key Transport Algorithm, based on Generic Hybrid Cipher

   id-ac-generic-hybrid OID ::= {
      is18033-2 asymmetric-cipher(1) generic-hybrid(2)
   }

   GenericHybridParameters ::= {
      kem  KeyEncapsulationMechanism,
      dem  DataEncapsulationMechanism
   }

   id-kem-rsa OID ::= {
      is18033-2 key-encapsulation-mechanism(2) rsa(4)
   }

   RsaKemParameters ::= {
      keyDerivationFunction  KeyDerivationFunction,
      keyLength              KeyLength
   }

   KeyDerivationFunction ::= AlgorithmIdentifier {{KDFAlgorithms}}

   KDFAlgorithms ALGORITHMS ::= {
      kdf2,
      ...  -- implementations may define other methods
   }

   KeyLength ::= INTEGER (1..MAX)

   DataEncapsulationMechanism ::= AlgorithmIdentifier {{DEMAlgorithms}}

   DEMAlgorithms ALGORITHM ::= {
      X9-SymmetricKeyWrappingSchemes,
      ...  -- implementations may define other methods
   }

   X9-SymmetricKeyWrappingSchemes ALGORITHM ::= {
      aes128-Wrap | aes192-Wrap | aes256-Wrap | tdes-Wrap,
      ...   -- allows for future expansion
   }

   -- Key Derivation Functions

   id-kdf-kdf2 OID ::= { is18033-2 key-derivation-functions(5) kdf2(2) }

   kdf2 ALGORITHM ::= {{ OID id-kdf-kdf2  PARMS KDF2-HashFunction }}

   KDF2-HashFunction ::= AlgorithmIdentifier {{KDF2-HashFunctions}}

   KDF2-HashFunctions ALGORITHM ::= {
      X9-HashFunctions,
      ...  -- implementations may define other methods
   }

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   -- Hash Functions

   X9-HashFunctions ALGORITHM ::= {
      sha1 | sha224 | sha256 | sha384 | sha512,
      ...  -- allows for future expansion
   }

   id-sha1 OID ::= {
      iso(1) identified-organization(3) oiw(14) secsig(3)
      algorithms(2) sha1(26)
   }

   id-sha256 OID ::= { nistAlgorithm hashAlgs(2) sha256(1) }
   id-sha384 OID ::= { nistAlgorithm hashAlgs(2) sha384(2) }
   id-sha512 OID ::= { nistAlgorithm hashAlgs(2) sha512(3) }

   sha1   ALGORITHM ::= {{ OID id-sha1    }} -- NullParms MUST be
   sha224 ALGORITHM ::= {{ OID id-sha224  }} -- accepted for these
   sha256 ALGORITHM ::= {{ OID id-sha256  }} -- OIDs
   sha384 ALGORITHM ::= {{ OID id-sha384  }} –- ""
   sha512 ALGORITHM ::= {{ OID id-sha512  }} –- ""

   -- Symmetric Key-Wrapping Schemes

   id-aes128-Wrap OID ::= { nistAlgorithm aes(1) aes128-Wrap(5)  }
   id-aes192-Wrap OID ::= { nistAlgorithm aes(1) aes192-Wrap(25) }
   id-aes256-Wrap OID ::= { nistAlgorithm aes(1) aes256-Wrap(45) }

   aes128-Wrap ALGORITHM ::= {{ OID id-aes128-wrap }}
   aes192-Wrap ALGORITHM ::= {{ OID id-aes192-wrap }}
   aes256-Wrap ALGORITHM ::= {{ OID id-aes256-wrap }}

   id-alg-CMS3DESwrap OBJECT IDENTIFIER ::= {
      iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9)
      smime(16) alg(3) 6
   }

   tdes-Wrap ALGORITHM ::= {{ OID id-alg-CMS3DESwrap  PARMS NullParms }}

B.4 Examples

   As an example, if the key derivation function is KDF2 based on
   SHA-256 and the symmetric key-wrapping scheme is the AES Key Wrap
   with a 128-bit KEK, the AlgorithmIdentifier for the RSA-KEM Key
   Transport Algorithm will have the following value:

      SEQUENCE {
         id-ac-generic-hybrid,                         -- generic cipher
         SEQUENCE {                           -- GenericHybridParameters
            SEQUENCE {                    -- key encapsulation mechanism
               id-kem-rsa,                                    -- RSA-KEM
               SEQUENCE {                            -- RsaKemParameters
                  SEQUENCE {                  -- key derivation function

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                     id-kdf-kdf2,                                -- KDF2
                     SEQUENCE {                     -- KDF2-HashFunction
                       id-sha256   -- SHA-256; no parameters (preferred)
                     },
                  16                              -- KEK length in bytes
                  },
            SEQUENCE {                   -- data encapsulation mechanism
               id-aes128-Wrap             -- AES-128 Wrap; no parameters
            }
         }
      }

   This AlgorithmIdentifier value has the following DER encoding:

      30 4f
         06 07 28 81 8c 71 02 01 02             -- id-ac-generic-hybrid
         30 44
            30 25
               06 07 28 81 8c 71 02 02 04                 -- id-kem-rsa
               30 1a
                  30 16
                     06 07 28 81 8c 71 02 05 02          -- id-kdf-kdf2
                     30 0b
                        06 09 60 86 48 01 65 03 04 02 01   -- id-sha256
                  02 10                                     -- 16 bytes
            30 0b
               06 09 60 86 48 01 65 03 04 01 05       -- id-aes128-Wrap


   The DER encodings for other typical sets of underlying components are
   as follows:

         *  KDF2 based on SHA-384, AES Key Wrap with a 192-bit KEK

            30 4f 06 07 28 81 8c 71 02 01 02 30 44 30 25 06
            07 28 81 8c 71 02 02 04 30 1a 30 16 06 07 28 81
            8c 71 02 05 02 30 0b 06 09 60 86 48 01 65 03 04
            02 02 02 18 30 0b 06 09 60 86 48 01 65 03 04 01
            19

         *  KDF2 based on SHA-512, AES Key Wrap with a 256-bit KEK

            30 4f 06 07 28 81 8c 71 02 01 02 30 44 30 25 06
            07 28 81 8c 71 02 02 04 30 1a 30 16 06 07 28 81
            8c 71 02 05 02 30 0b 06 09 60 86 48 01 65 03 04
            02 03 02 20 30 0b 06 09 60 86 48 01 65 03 04 01
            2d

         *  KDF2 based on SHA-1, Triple-DES Key Wrap with a 128-bit KEK
            (two-key triple-DES)

            30 4f 06 07 28 81 8c 71 02 01 02 30 44 30 21 06
            07 28 81 8c 71 02 02 04 30 16 30 12 06 07 28 81

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            8c 71 02 05 02 30 07 06 05 2b 0e 03 02 1a 02 10
            30 0f 06 0b 2a 86 48 86 f7 0d 01 09 10 03 06 05
            00

         *  KDF2 based on SHA-224, Triple-DES Key Wrap with a 192-bit
            KEK (three-key triple-DES)

            [[to be defined, awaiting OID for SHA-224]]


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